Quantum based information transmission system and method

ABSTRACT

A method and system of data transmission; the method comprising: converting data into qubits; transmitting a first qubit; measuring the first qubit at receiver location; determining whether or not to transmit portions of data from a sequential successive qubit based upon the value of the first qubit measured at the receiver location. The system comprising a sender and at least one receiver, the sender comprising: a converter for converting data into qubits; a modulator for modulating a signal based upon the values of the qubits; a transmitter for transmitting the modulated signal to at least one receiver; the at least one receiver comprising: a detector for measuring the value of at least one qubit; a feedback circuit for transmitting the measured value of the at least one qubit to the sender; whereby the transmission of data for each successive qubit is based upon the value measured for the preceding qubit and the sender utilizes only the data for each successive qubits which correlates to the measured value of the preceding qubit.

RELATED APPLICATIONS

This application claims priority of U.S. Nonprovisional application Ser.No. 11/196,738, filed Aug. 4, 2005, which issued as U.S. Pat. No.7,660,533 on Feb. 9, 2010, and U.S. Provisional Patent Application Ser.No. 60/598,537 filed Aug. 4, 2004, both of which are incorporated hereinby reference.

GOVERNMENT INTEREST

The invention described herein may be manufactured, used, and licensedby or for the United States Government.

FIELD OF THE INVENTION

This invention relates in general to methods and apparatus forprocessing, compression, and transmission of data based upon quantumproperties and in particular to high density transmission of data.

BACKGROUND OF THE INVENTION

Quantum computing represents a revolutionary frontier technologyundergoing intense development. Quantum computing for example, mayrender classically intractable computations feasible. In spite oftheoretical calculations showing enormous efficiency increases forquantum computers relative to classical computers, such improvementshave made slow progress. Yet, the societal implications of datacompression and transmission based on quantum computing algorithms areconsiderable. Transmission of voice, image, video and holographicsignals in a lossy, extremely highly compressed format would impactnearly every field of human endeavor. As the usage of cell phones,television signals and internet communications crowds the bandwidthavailable, there exists a need for compression of data communications.

Quantum communication involves qubits, which are quantum bits or unitsof quantum information. A qubit may be visualized by a state vector in atwo-level quantum-mechanical system. Unlike a classical bit, which canhave the value of zero or one, a qubit can have the values of zero orone, or a superposition of both. A qubit may be measured in basis states(or vectors) and a conventional Dirac is used to represent the quantumstate values of zero and one herein, as for example, |0

and |1

. The “pure” qubit state is a linear superposition of those two statescan be represented as combination of |0

and |1

or q_(k)=A_(k)|0

+B_(k)|1

, or in generalized form as A_(n)|0

and B_(n)|1

where A_(n) and B_(n) represent the corresponding probability amplitudesand A_(n) ²+B_(n) ²=1. Unlike classical bits, a qubit can exhibitquantum properties such as quantum entanglement, which allows for highercorrelation than that possible in classical systems. When entangledphoton pairs are split, the determination of the state (such aspolarization or angular momentum) of one of the entangled photons ineffect determines the state of the other of the entangled photon pair;since entangle photon pairs are the conjugates of one another. Anexample of a visualization of a series of qubits is depicted in FIG. 1;a schematic depicting a prior art three qubit quantum binary tree toillustrate an information storage index space equivalency to eightclassical bits. The quantum binary tree of FIG. 1 is depicted for 3qubits which provides an index space of 8.

SUMMARY OF THE INVENTION

The present inventive method allows for the transmission of informationover a path wherein the data or information is first converted toqubits. A quantum tree formed of qubits is depicted in FIGS. 1, 1A, 1Band 1C. In the example shown, 3 qubits are used. However, the number ofqubits may be changed without departing from the scope and principles ofthe present invention. As the first qubit is transmitted, a measurementtakes place and the result is inputted into computer 207, illustrated inFIG. 2, et seq. Based upon this measurement, as illustrated by thedecision tree of FIG. 1A, either the left (L) or right (R) portion ofqubit 2 is not used (or transmitted). Following the transmission of theportion of qubit 2, another measurement takes place and the result isinputted into computer 207. Based upon this measurement, as illustratedby the decision tree of FIG. 1B, either branch A1 or A2 is followed. Inthe example shown in FIG. 1C, where the first and second measured valueswere zeroes, the qubit portions represented by the nodes at the dottedline branches are unused and not transmitted.

Due to the properties of the qubits, a preferred embodiment systememploys the quantum Fourier transform (QFT) and a classical or quantuminverse Fourier transform in the measurement process. Data inputted inthe form of a wave function, generated using, for example, amplitudes ofa given signal, is converted into a quantum state or qubits over which,in a preferred embodiment of the present invention, transforms, such asthe quantum Fourier transform (QFT), operate. The conversion of the wavefunction to a quantum state represented by qubits is described, forexample, in GuiLong, Yang Sun; “Efficient scheme for initializing aquantum register with an arbitrary superposed state,” Physical Review A,Volume 64, 014303, hereby incorporated by reference). The quantumFourier transform is implemented by a series of optical elementsimplementing quantum operations followed by a measurement as describedfor example, in Robert B. Griffiths, et al. “Semiclassical FourierTransform for Quantum Computation,” Physical Review Letters, Apr. 22,1996, hereby incorporated by reference). Although a particularembodiment is described, other equivalent formulations, processes, andconfigurations are encompassed within the scope of the invention.

In terms of data flow, a preferred methodology comprises splitting awave function representative of an input data set into an arbitrarilyoriented elliptical polarization state and a comparator wave functionstate, the comparator wave function state being transmitted to adetector. In a preferred embodiment, a quantum Fourier transform isperformed on the arbitrarily oriented elliptical polarization state toyield a quantum computational product. A quantum Hadamard transform isperformed on the quantum computational product to yield one of twopossible quantum particle outputs. Through feedback circuitry, the inputdata set is processed based upon the coincident arrival of thecomparator wave function state and one of the two quantum particleoutputs. Data compression and transmission in accordance with apreferred embodiment of the present invention may be performed on eithera quantum computer or a digital computer.

A data communication system operating on quantum computation principlesincludes a light source having a photon output coding an input data set.A Type-I or Type-II nonlinear crystal converts the photon output into anentangled photon output. An arbitrarily oriented polarization state isassured by passing the entangled photon output through a polarizationmodulator (44) and a phase modulator (46). A polarization interferometer(122) performs a controlled phase shift transform on the arbitrarilyoriented polarization state as an interferometer output. A halfwaveplate then performs a quantum. Hadamard gate transform to generate oneof two possible photon states from the interferometer output thuscompleting the operations required for a quantum Fourier transform.Coincidence electronics reconstruct the input data set a distance fromthe light source. The reconstruction is based on the coincident arrivalof the one of two possible photon states and at least one of theentangled photon output or the interferometer output. The result is thenfed back via computer 207 and associated circuitry whereupon thecomputer 207 in conjunction with polarization modulator (44) and a phasemodulator (46), based upon the “branch” determinations, processes onlyportions of the succeeding qubits, resulting in reduction in the amountof data which is transmitted.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic depicting a three qubit quantum binary tree toillustrate an information storage index space equivalency to eightclassical bins.

FIG. 1A is schematic depiction of the first level branching of the threequbit quantum binary tree of FIG. 1

FIG. 1B is schematic depiction of the second level branching of thethree qubit quantum binary tree of FIG. 1

FIG. 1C is schematic depiction of the third level branching of the threequbit quantum binary tree of FIG. 1.

FIG. 2 is a schematic of an optical bench configured as a quantumcomputer system according to the present invention using a Type-IInonlinear optics crystal and a polarization Mach-Zehnder interferometerto perform a quantum Fourier transform (QFT);

FIG. 3 is a schematic of an optical bench configured as a quantumcomputer system according to the present invention using a Type-IInonlinear optics crystal and a polarization Mickelsen interferometer toperform a QFT;

FIG. 4 is a schematic of an optical bench configured as a quantumcomputer system according to the present invention using a Type-IInonlinear optics crystal and a polarization Sagnac interferometer toperform a QFT;

FIG. 5 is a schematic of an optical bench configured as a quantumcomputer system according to the present invention using a Type-Inonlinear optics crystal and a polarization Mach-Zehnder interferometerto perform a QFT;

FIG. 6 is a schematic of an optical bench configured as a quantumcomputer system according to the present invention using a Type-Inonlinear optics crystal and a polarization Mickelsen interferometer toperform a QFT;

FIG. 7 is a schematic of an optical bench configured as a quantumcomputer system according to the present invention using a Type-Inonlinear optics crystal and a polarization Sagnac interferometer toperform a QFT; and

FIG. 8 is a series of 32 normalized sound spectrum samples depicted as aquantized histogram of amplitudes, black line and gray line overliesdenoting classical and quantum Fourier transforms of the sample,respectively.

FIG. 9 is a broad block diagram of a system embodying the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention has utility in data transmission. A quantumcomputing algorithm for processing data has greater than classicalefficiency when run on a quantum computer. It is appreciated that anembodiment of the present invention comprises a method for datacompression and transmission that is operative in a classical digitalcomputing environment although without the superior speed andinformation storage properties of qubits that are realized on a quantumcomputer. While the present invention is hereafter detailed in thecontext of sound compression and transmission, it is appreciated thatdata corresponding to any number of media are equally well suited fortransmission in a highly compressed and lossy manner, such as lighttransmission. Data set types other than sound readily transmittedaccording to the present invention illustratively include images, video,holograms, digital instrument output and numerical streams.

A preferred embodiment of the present invention includes a system forthe transmission and reconstruction of a data set through theutilization of a quantum Fourier transform (QFT) operation on qubitscoding the data set.

A preferred embodiment of the present invention prepares a wave functionin a n data set; as described for example in Long and Sun; “Efficientscheme for initializing a quantum register with an arbitrary superposedstate, “Physical Review A, vol. 64, Issue 1, 014303 (2001) (hereinafter“Long and Sun”). In “Long and Sun,” a scheme is presented that can mostgenerally initialize a quantum register with an arbitrary superpositionof basis states as a step in quantum computation and quantum informationprocessing. For example, “Long and Sun” went beyond a simple quantumstate such as |i₁, i₂ i₃, . . . i_(n)

with i_(j) being either 0 or 1, to construct an arbitrary superposedquantum state. “Long and Sun” utilize the implementation of O(Nn²)standard 1- and 2-bit gate operations, without introducing additionalquantum bits. The terminology arbitrary superposed quantum state as usedherein correlates to the construction of an arbitrary superposed quantumstate as described, inter glia, in “Long and Sun.”

As depicted in FIG. 2, a series of optical elements are provided to actas quantum operators followed by a measurement to implement the quantumFourier transform. R. B. Griffiths, C.-S. Niu; Physical Review Letters76, 3328-3231 (1996). An optical bench with appropriate electronics iswell suited to function as a quantum computer for the compression andtransmission of data corresponding to sound. Those of ordinary skill inthe art can appreciate that although an optical bench is described asthe platform for generating and performing operations on qubits, it isappreciated that three plus qubit quantum computers are known to the artbased on ion trapping and the nuclear magnetic resonance spectrometer.

An inventive quantum computing system has been developed for dataprocessing. The data set amplitudes, such as sound amplitudes, arerepresented by a quantum wave function. The wave function is in turncoded into the qubits of quantum particles. Preferably, the quantumparticles are photons, but trapped ions or magnetic spin states can alsobe utilized to practice the principles of the present invention.

In the practice of the present invention on a classical computer, thedata series, that for illustrative purposes is a sound, is broken into aseries of segments each represented by the number of qubits that theclassical computer can store and compute. In a quantum computer, thequantum particles, preferably photons, are operated on by opticalcomponents to perform the inventive method steps.

The method of the present invention relies on the use of qubits in aquantum computer or the simulation of qubits in a classical computer.Qubits comprise superpositions of ones and zeros where bothsimultaneously exist. Photons that define the wave function aresubjected to a quantum Fourier transform operation. In the process, thephotons are measured thereby destroying the quantum state, but providingthe measured probability in terms of the wave function and its complexconjugateP=ψψ*.  (1)

An inverse Fourier transform (FT) is then applied to the square root ofthe measured probability to recover a lossy intelligible datacompression in the form of quantum particle detection. It is appreciatedthat the inverse Fourier transform may be either a classical or quantumtransform. A classical fast Fourier transform is readily performed byoptical bench elements or through a classical computer program. Theforward and inverse transforms are conducted using a relatively smallsample of the wave function Fourier modes which has the property ofpreserving much of the intelligibility of the data while providing acompression and communication efficiency. Using the quantum computingsimulation of a classical computer according to the present invention, asound data set (for example) is intelligibly reproduced with a lossycompression factor over a classical computation. Computationalefficiency with the present invention increases in the case of anincreasing set of qubits. In practice, the inventive method allows forthe transmission of information over a long path using a small number ofphotons. Data transmission with a small number of photons carrying thedata in a quantum particle form is amenable to free optical pathtransmission through air or vacuum, through optical fibers and viasatellite transmission. As a result, a first location remote from asecond location is retained in communication therebetween with thetransmission of a comparatively small number of qubits of quantumparticles relative to the data exchanged. Photons are amenable totransit in an environment exposed to climactic weather between thelocations. It is appreciated that co-linear transmission of a comparatorwave function state and an information carrying state facilitateslong-range data transmission.

State Preparation

According to the present invention, a data set is modeled by, or in theform of, a wave function. By way of example, a sound is characterized byintensity amplitudes at uniformly spaced intervals

$\begin{matrix}{{\alpha_{i} = {\alpha\left( t_{i} \right)}}{where}} & (2) \\{t_{i} = {t_{0} + {\sum\limits_{j = 1}^{i}{\Delta\;{t_{j}.}}}}} & (3)\end{matrix}$

A superimposed quantum form is applied to the sound data set tofacilitate quantum computer manipulation. To accomplish thequantification, data amplitudes are equated to a wave function in theform of a series

$\begin{matrix}{{\psi = {\sum\limits_{i = 0}^{2^{N} - 1}{\alpha_{i}\left. i \right\rangle}}}{where}} & (4) \\\left. i \right\rangle & (5)\end{matrix}$

is the quantum state key. The qubits are characterized as the quantumstate superpositionsq _(k) =A _(k)|0

+B _(k)|1

.  (6)A quantum probability conservation condition is imposed such thatA _(n) ² +B _(n) ²=1.  (7)

To account for the quantum superposition, the quantum data is organizedin terms of a conventional quantum binary tree. A prior art quantumbinary tree is depicted as a branching between 0 and 1 outcomes forsuccessive steps in FIG. 1. Using the qubit representation shown in FIG.1, the first step is to determine whether a one or zero exists at thefirst branch located at the top of the triangle depicted in FIG. 1A. Ifa zero value is present, Branch A is followed and the right side of thetriangle or the “Branch B” becomes unnecessary to future determinations.Elimination of the “B Branch” results in data compression. FIG. 1B is adepiction of the second level branching following the determinationdepicted to the left in FIG. 1A. If the value is zero, Branch A1 isfollowed. If the value is one, Branch A2 is followed. In each case, theother branch is eliminated resulting in data compression. FIG. 1C is adepiction of the third level branching following the determinationdepicted to the left in FIG. 1B. If the value is zero, Branch A4 isfollowed. If the value is one, Branch A5 is followed. In each case, theother branch is eliminated resulting in further data compression. Theparticular values selected for depiction in FIGS. 1B and 1C are merelyexemplary. Results a “one” determination at first level are not shown inFIG. 1B to make the diagram easier to follow. Results of a “one”determination at the second level are not shown in FIG. 1C to make thediagram easier to follow.

The outcomes of the successive steps sum to the values 0 through2^(n)−1, where n is the number of qubits. The means of obtaining the 0or 1 depends on the specific experimental and corresponding simulationimplementation. There are several conventional rules that are possiblefor determining the 0 or 1 value. For example, a 0 state may correspondto a horizontal measurement and the 1 may correspond to a verticalmeasurement, or the reverse may be true. In general, the series of qubitmeasurements are prepared such that each value of the state preparationis conditioned to determine the 0 or 1 at each branch. An alternatequbit architecture operative herein is termed “winner take all.” In thesimulation depicted in FIG. 1, n qubit measurements are made. The nvalue is determinative of the first branch. The 2″ are divided into twoparts, lower 0 to ((2^(n)/2)−1 and higher indices ((2^(n)/2) to 2^(n)−1.The side with the greatest sum of the indices measured determines thepath of the first branch. The second level branch has one half thenumber of indices of the first branch. Consecutive indices assigned arefrom the selected half from the first branch. The same process is usedfor the second branch level as from the first branch, but with half ofthe indices. This process repeats until all the branching is determinedand the selected single index is determined. The quantum binary treedepicted in prior art FIG. 1 for three qubits provides an index space ofeight. The quantum binary tree is expandable to n qubits which isequivalent to an index space of 2^(n) over which transforms, such as theQFT operate.

The quantum superposition amplitudes at any qubit level in the binarytree may be constructed from sound amplitudes

$\begin{matrix}{A_{k} = {\sum\limits_{i = 0}^{i = {\frac{2^{n}k}{2} - 1}}\alpha_{1}}} & (8)\end{matrix}$where the summation is over the number of statesn _(k)  (9)at each level of the quantum binary tree. Similarly

$\begin{matrix}{B_{k} = {\sum\limits_{i = \frac{2^{n}k}{2}}^{i = {{2^{n}k} - 1}}{\alpha_{1}.}}} & (10)\end{matrix}$The amplitudes α are approximated in the quantum computation byidentification with probabilities which can then be sampled. For onerealization, it is noted that

$\begin{matrix}{{\alpha_{0} = {\prod\limits_{i = 0}^{i = {{2^{n}k} - 1}}\; A_{i}}}{and}} & (11) \\{\alpha_{k} = {\prod\limits_{i = 0}^{i = {{2^{n}k} - 1 - j}}\;{\prod\limits_{j = 0}^{j = i}\;{A_{i}{B_{j}.}}}}} & (12)\end{matrix}$The classical index k is given in terms of the quantum qubit indices nof the quantum binary tree made of n qubits

$\begin{matrix}{k = {\sum\limits_{i = 0}^{i = {n - 1}}{\left( 2^{n - i} \right){\left\langle {q_{1}} \right\rangle.}}}} & (13)\end{matrix}$The term

|q _(i)|

  (14)represents the measurement of the i^(th) qubit, registering as a 0 or 1.

Quantum Data Simulation

Superpositions of qubits are used to store and process data such assound. The amplitude of the “data” can be stored as the amplitudes of asuperposed quantum stateω=Σα_(i) |k

_(i).  (15)where |k

is the eigenstate of Ψ. The term

can be decomposed as a direct product of qubits|q

₁

|q

₂

. . .

|q

_(n)  (16)which compacts storage requirements by a factor of log 2 relative to aclassical computation. A data set of size 2^(n) can be stored andoperated on in n quantum bits. Mathematical transforms can also beperformed on the quantum stored signal with the associated computationalsavings.

Quantum Computational System

According to the present invention, data compression and transmissionare preferably performed using photons as quantum particle qubits.Various system configurations are depicted in accompanying FIGS. 2-7where like numerals described with reference to subsequent figurescorrespond to previously detailed elements.

Referring now to FIG. 2, an inventive system is depicted generally at10. A data encoder 12 converts the data set to a set of photonic qubitsthat satisfies the expression of Equation 15 and triggers a light source14 accordingly. Preferably, the light source 14 is a laser. Exemplarylasers operative herein illustratively include Nd:YAG, ion lasers, diodelasers, excimer lasers, dye lasers, and frequency modified lasers.Photons 16 emitted from the light source 14 are optionally passedthrough a spatial filter 18. Filter 18 converts the photons 16 in animage space domain to a spatial frequency domain and serves the purposeof removing, for example, stripe noise of low frequency and/or highfrequency noise. The noise associated with system fluctuationsillustratively including line noise powering the light source 14,thermal gradients, detector noise, and inherent quantum noise. Thephotons 20 having passed through spatial filter 18 are then passedthrough a Type-II nonlinear optics crystal 22. Type-II nonlinear opticcrystals are well known to the art and illustratively include potassiumdihydrogen phosphate, potassium titanyl phosphate, beta-barium borate,cesium lithium borate and adamantyl amino nitro pyridine. A dichroicmirror 24 is used to selectively reflect out of the beam path 26 thosephotons 28 that have changed wavelength as a result of passing throughthe crystal 22. A beam stop 30 blocks the path of photons 28. Theentangled photons 26 are split by interaction with a polarization beamsplitter 32. The entangled photons 26 are split into a known photonstate 34 and a comparator wave function state 36. The comparator wavefunction state 36 is directed onto a single photon counting module 38 byan optional mirror set 40. It is appreciated that a reorganization ofbeam paths in the system 10 obviates the need for mirror set 40. Thedetection of the comparator wave function state 36 by the single photoncounting module 38 is fed to coincidence electronics 42 and is used toreconstruct the data set. The known photon state 34 is then passedthrough a polarization modulator 44 and a phase modulator 46. Exemplarypolarization phase modulators illustratively include liquid crystals,Kerr cells, and Pockel cells. Preferably, a series of two liquid crystaldevices and a quarter wave plate are used to achieve arbitrarypolarization. Upon the known photon state 34 interacting with thepolarization and phase modulators 44 and 46, respectively, the knownphoton state 34 is transformed into an arbitrarily oriented ellipticalpolarization state 48 based on the data set signal being transformed andany previously measured photon state, if any is known. The arbitrarilyoriented elliptical polarization state 48 is optionally reflected from amirror 50 and then enters a polarization interferometer depictedgenerally at 60. The interferometer 60 depicted has the geometry of apolarization Mach-Zehnder interferometer and includes a polarizationbeam splitter 62 that transmits one portion 64 to a phase modulator 66resulting in a phase shift in the light component 68 reachingpolarization beam splitter 70 relative to the other polarizationcomponent 72. Polarization beam splitter 70 recombines beam components68 and 72 to complete a controlled phase shift transform on therecombined state 74 from the interferometer 60. Ancillary mirrorscollectively numbered 76 are provided to reflect light in desireddirections. The controlled phase shift transformed light componentrepresenting a recombined phase state 74 then interacts with a half waveplate oriented at 22.5 degrees 78 in order to implement a quantumHadamard gate transformation therein and thus complete a quantum Fouriertransform. The half wave plate 78 provides a qubit prioritized input 80to a polarization beam splitter 82.

The process that computes the Quantum Fourier Transform (QFT) of asignal may be described as follows. First, the computer or device thatholds the signal divides the signal into a series of sections. Eachsection contains N samples of the signal. This section of N samples isthen used to prepare the first qubit of the quantum state using aprescribed technique for the QFT. This quantum state is then passedthough a device that applies a particular phase shift appropriate tothis qubit of the QFT. The qubit is then measured and the result of thatmeasurement is recorded as a 0 or 1. This measurement is also used todetermine which half of the N samples of the current signal section areused as a subsection to prepare the next qubit, the other half is notneeded to prepare the next qubit. This qubit and all the remainingqubits generated for the original signal section are prepared andmeasured in a similar way with each qubit measurement using only half ofthe remaining signal subsection to prepare the next qubit. This processends when the last qubit that is prepared using only 2 samples of thesignal section. When all these qubits have been measured for one sectionwe have a binary number that tells us to add 1 to the bin addressed bythat binary number, for instance the binary number 010 would indicateaddress 2 and the binary number 110 would indicate address 6. Thesesteps are repeated a number of times on the same signal section togenerate a power spectrum representation of the signal section. Signalprocessing techniques such as a classical inverse Fourier transform orcompressive sensing/sampling can used on this power spectrum toreconstruct the initial signal section in a lossy but still recognizablemanner.

In the QFT a number of photons, each with prepared qubit states, aresent sequentially through quantum controlled phase transforms followedby quantum Hadamard transforms. The state preparation is accomplished bysetting the values of the phase and setting the photons to particularelliptical polarization values.

The Hadamard transform is a quantum transform operating on one qubit ata time. The Hadamard gate transform is given as

$\begin{matrix}{\begin{pmatrix}1 & 1 \\1 & {- 1}\end{pmatrix}.} & (17)\end{matrix}$The qubits are operated on by the Hadamard transform as|q _(n) _(k) ′

=H|q _(n) _(k)

  (18)where n_(k) is the index of the current qubit state.

Hadamard transforms in the order of the most significant qubit to theleast significant qubit.

The initial state of each photon qubit is conditioned on the measuredvalues of each photon that went before.

A single photon is operated upon by a Hadamard transform, with theeffect of Hadamard transforms on multiple photons representing an entirewave function is represented by the combined Hadamard transform.

Wave Function Transform

The total wave function made of arbitrary superposed states is operatedon by the combined Hadamard transform|ψ′

=Ĥ _(gate)|ψ  (19)whereĤ _(gate) =H

I . . .

I.  (20)Here the direct product of the identities is repeated until all of thequbits are taken into account.

Single photon counting modules 84 and 86 count individual photons with agiven polarization and report a counting event to coincidenceelectronics 42. Only when coincidence is noted between a photon countingevent at module 38 and 84, or between module 38 and module 86 is thecount considered a valid probability density function measurement. Theprobability density function is defined byP=ψψ*  (21)and sets the number of times on the average that a photon lands in anindexed space interval. For n qubits there are 2^(n) indexed spaceintervals.

A determination as to the polarization of each photon is provided bysignal measurement at one of the single photon counting modules 84 and86. The polarization of each photon is measured at the end of the photonpath through the Hadamard gate and electro-optics. If horizontal (0)then no phase operations applies to the remaining qubits. Otherwise, acontrolled phase operation R_(m) is applied to remaining operations. TheR_(m) set is defined as

$\begin{matrix}{R_{m} = {\begin{pmatrix}1 & 0 \\0 & {\mathbb{e}}^{\frac{i\;\pi}{2^{\Delta\; n}}}\end{pmatrix}.}} & (22)\end{matrix}$

The term Δn represents the distance between the n_(k) indices of thebinary tree levels under consideration,Δn=n _(k) −n _(k′)  (23)

The output of an inventive system is provided to a buffer store. Fromthe buffer store it may be provided to an output device on either areal-time or delayed basis as still images, video images, movies, audiosound representations, and the like.

Referring now to FIG. 3 where an inventive system is depicted generallyat 90, the system 90 has numerous features in common with that systemdepicted in FIG. 2 and such attributes share like numerals with thosedetailed with respect to FIG. 2. In contrast to system 10 depicted inFIG. 2, the system 90 includes an interferometer shown generally at 92that has the geometry of a polarization Mickelsen interferometer. Theinterferometer 92 receives an arbitrarily oriented ellipticalpolarization state 48 incident on a polarization beam splitter 62 thatsplits the arbitrarily oriented elliptical polarization state 48 withone component of the polarization 93 phase shifted at phase modulator 94relative to the other polarization component 96. The polarizationcomponent 96 interacts with a quarter wave plate 98 rotatingpolarization by 90 degrees. Phase component 96 is then reflected frommirror 100 back to polarization beam splitter 62 where the phasecomponent 96 is recombined with phase shifted polarization component 93that has passed through polarization modulator 94, a quarter wave plate102 rotating the polarization by 90 degrees and returning topolarization beam splitter through reflection from translating mirror104. It is appreciated that the phase modulator 94 is readily removedand the phase difference applied to phase shifted polarization component93 is imparted by the translating mirror 104. Regardless of the specificcomponents of interferometer 92, the recombined state 74 is reflectedoff mirror 76 and further manipulated as detailed with respect to FIG. 2such that a valid probability density function measurement is onlycounted upon coincidence between photon detection at modules 38 and 84,or between modules 38 and 86.

Referring now to FIG. 4, an inventive system is depicted generally at120, the system 120 has numerous features in common with that systemdepicted in FIG. 2 and such attributes share like numerals with thosedetailed with respect to FIG. 2. In contrast to system 10 depicted inFIG. 2, the system 120 includes an interferometer shown generally at 122that has the geometry of a polarization Sagnac interferometer. Thearbitrarily oriented elliptical polarization state 48 is split atpolarization beam splitter 62 to phase shift a polarization component123 through interaction with a phase modulator 94. A second component126 is recombined with the phase shifted component 123 throughcoincidental reflection with the mirrors collectively labeled 128. Therecombined state 74 is reflected by mirror 76 onto a half wave plate 78to implement a quantum Hadamard gate transformation.

Single photon counting modules 84 and 86 count individual photons with agiven polarization and report a counting event to coincidenceelectronics 42. Only when coincidence is noted between a photon countingevent at module 38 and 84, or between module 38 and module 86 is thecount considered a valid probability density function measurement.

Referring now to FIG. 5, an inventive system is depicted generally at140 that is a Type-I nonlinear optics crystal analog in the system 10depicted with reference to FIG. 2, where like numerals used withreference to FIG. 5 correspond to the description of those previouslyprovided with respect to FIG. 2. A Type-I nonlinear crystal 142generates entangled photon pairs with the same known polarization fromphotons 20. Type-I nonlinear optical crystals operative hereinillustratively include beta-barium borate, potassium niobate, lithiumtriborate and cesium lithium borate. Preferably, the crystal 142 istuned for non-degenerative down conversion with regard to dichroicmirror 144. The entangled photon pair with same known polarization 146is separated from frequency shifted components 145 that are in turnterminated at beam stop 30. The monochromatic known polarization beam148 is incident on polarization beam splitter 32 and that component witha known photon state 150 is directed through a polarization modulator44, a phase modulator 46 to yield an arbitrarily oriented polarizationstate 158 that is optionally reflected off mirror 50 and intointerferometer 60 that has the geometry of a polarization Mach-Zehnderinterferometer. Second photon state 156 is directed onto beam stop 160.The arbitrarily oriented elliptical polarization state 158 retainscharacteristics of the data set signal to be subsequently transformed inany previously measured photon state, if such is known. Theinterferometer 60 depicted has the geometry of a polarizationMach-Zehnder interferometer and includes a polarization beam splitter 62that transmits one portion 162 to a phase modulator 66 resulting in aphase shift in the light component 168 reaching polarization beamsplitter 70 relative to the other polarization component 170.Polarization beam splitter 70 recombines beam components 168 and 170 tocomplete a quantum Fourier transform on the recombined state 172 fromthe interferometer 60. Ancillary mirrors collectively number 76 areprovided to reflect light in desired directions. The recombined state172 is such that one of the photons of an entangled photon pair isreflected by dichroic mirror 144 to single photon counting module 38while the other photon of the entangled photon pair will be transmittedonto the half wave plate 78.

Single photon counting modules 84 and 86 count individual photons with agiven polarization and report a counting event to coincidenceelectronics 42. Only when coincidence is noted between a photon countingevent at module 38 and 84, or between module 38 and module 86 is thecount considered a valid probability density function measurement. It isappreciated that a co-linear transmission of the combined state 172 orthe arbitrarily oriented polarization state is well suited for remotetransmission between the light source 14 and coincidence electronics 42.

Referring now to FIG. 6, a Type-I nonlinear optical crystal analogsystem is depicted in general at 180 relative to system 90 of FIG. 3,where like numerals used with reference to FIG. 5 correspond to thedescription of those previously described with respect to the proceedingfigures. A Type-I nonlinear crystal 142 generates entangled photon pairswith the same known polarization from photons 20. Preferably, thecrystal 142 is tuned for non-degenerative down conversion with regard todichroic minor 144. The entangled photon pair with same knownpolarization 146 is separated from frequency shifted components 145 thatare terminated at beam stop 30. The monochromatic known polarizationbeam 148 is incident on polarization beam splitter 32 and that componentwith a known photon state 150 is directed through a polarizationmodulator 44, a phase modulator 46 to yield an arbitrarily orientedelliptical polarization state 158 that is reflected off minor 50 andinto an interferometer shown generally at 92 that has the geometry of apolarization Mickelsen interferometer. The interferometer 92 receivesthe arbitrarily oriented elliptical polarization state 158 incident on apolarization beam splitter 62 that splits the arbitrarily orientedelliptical polarization state 158 with one component of the polarization183 phase shifted at phase modulator 94 relative to the otherpolarization component 186. The polarization component 186 interactswith a quarter wave plate 98 rotating polarization by 90 degrees. Phasepolarization component 186 is then reflected from mirror 100 back topolarization beam splitter 62 where the phase component 186 isrecombined with phase shifted polarization component 183 that has passedthrough polarization modulator 94, a quarter wave plate 102 rotating thepolarization by 90 degrees and returning to polarization beam splitterthrough reflection off of translating mirror 104. Second photon state156 is directed onto beam stop 160. The arbitrarily oriented ellipticalpolarization state 158 retains characteristics of the data set signal tobe subsequently transformed in any previously measured photon state, ifsuch is known. The combined state 187 is transmitted through a half waveplate 78 oriented at so as to perform a quantum Hadamard transform toyield recombined transformed output 189. The recombined transformedoutput 189 is such that one of the photon components thereof isreflected by dichroic mirror 144 to single photon counting module 38while the other photon component is carried to beam splitter 82 to yielda single photon registered on one of the single photon counting modules84 or 86.

Single photon counting modules 84 and 86 count individual photons with agiven polarization and report a counting event to coincidenceelectronics 42. Only when coincidence is noted between a photon countingevent at module 38 and 84, or between module 38 and module 86 is thecount considered a valid probability density function measurement.

Referring now to FIG. 7, a Type-I nonlinear optical crystal analogsystem is depicted in general at 200 relative to system 120 of FIG. 4,where like numerals used with reference to FIG. 4 correspond to thedescription of those previously described with respect to the proceedingfigures. A Type-I nonlinear crystal 142 generates entangled photon pairswith the same known polarization from photons 20. Preferably, thecrystal 142 is tuned for non-degenerative down conversion with regard todichroic mirror 144. The entangled photon pair with same knownpolarization 146 is separated from frequency shifted components 145 thatare terminated at beam stop 30. The known polarization beam 148 isincident on polarization beam splitter 32 and that component with aknown photon state 150 is directed to a polarization modulator 44. Thepolarization modulator 44 and phase modulator 46 are controlled bycomputer 207, which determines which half of the data to process basedupon the last measurement fed back from coincident detector 42, which isconnected to the computer 207 by lines 209 and 110. The component with aknown photon state is directed through a polarization modulator 44 andphase modulator 46 to yield an arbitrarily oriented ellipticalpolarization state 158 that is reflected off mirror 50 and into aninterferometer shown generally at 122 that has the geometry of apolarization Sagnac interferometer. The interferometer 122 receives thearbitrarily oriented elliptical polarization state 158 incident on apolarization beam splitter 62 that splits the arbitrarily orientedelliptical polarization state 158 to phase shift a polarizationcomponent 203 through interaction with a phase modulator 94. PhaseModulator 94 is also connected to computer 207 by lines 208 and 210. Thecomputer 207 controls the phase modulator 94 depending upon the stage ofthe Fourier transform. Optionally, a second computer 211 may be used tocontrol phase modulator 94 if the phase modulator is at a remotelocation. The second component 206 is recombined with the phase shiftedcomponent 203 through coincidental reflection with the mirrorscollectively labeled 128. Second photon state 156 is directed onto beamstop 160. The arbitrarily oriented elliptical polarization state 158retains characteristics of the data set signal to be subsequentlytransformed in any previously measured photon state, if such is known.The combined state 187 is transmitted through a half wave plate 78oriented at so as to perform a quantum Hadamard transform to yieldrecombined transformed output 189. The recombined transformed output 189is such that one of the photon components thereof is reflected bydichroic mirror 144 to single photon counting module 38 while the otherphoton component is carried to beam splitter 82 to yield a single photonregistered on one of the single photon counting modules 84 or 86.

Single photon counting modules 84 and 86 count individual photons with agiven polarization and report a counting event to coincidenceelectronics 42. Only when coincidence is noted between a photon countingevent at module 38 and 84, or between module 38 and module 86 is thecount considered a valid probability density function measurement. Thecoincidence electronics 42 feed the result back to the computer 207 vialines 209 and 210 so that the computer 207 determines which portion ofthe data to process next and how to prepare the data bases on the lastmeasurement detected by the coincidence electronics. This feature isdepicted in FIG. 1A where dotted lines are used to show data paths whichare no longer in use and the 4 BINS labeled R are no longer used, whilethe 4 BINS labeled L remain to be processed. By making a determinationnot to use the 4 BINS labeled R as depicted in FIG. 1A, data compressionis achieved.

FIG. 9 is a broad block diagram depicting an embodiment of the presentinvention. Broadly, in the system of FIG. 9, a classic computer 12A (ora classical computer with devices as described in FIGS. 2-7) is loadedwith an input signal 10A. The system 12A then performs a quantum Fouriertransform and either a classical inverse Fourier transform or a quantuminverse Fourier transform. The output of system 12A is provided to abuffer store 14A. From the buffer store it may be provided to an outputdevice 16A on either a real time or delayed basis as still images, videoimages, movies, audio sound representations, and the like.

Example Sound Spectrum Computation

In order to evaluate the ability of the inventive quantum algorithm tocompress and transmit a signal representative of the data set with acomparatively small number of photons, 32 sound samples defining anormalized arbitrary spectrum are provided in the top left panel of FIG.8. The histogram defines a quantized spectrum while the solid linessuperimposed thereover represent classical Fourier (gray line) transformand QFT (black line) fits to the data. The 32 sound sample elements ofthe top left spectrum are amenable to storage and operation on 2^(n) or5 qubits. The top right panel of FIG. 8 represents a single statisticalevaluation of the arbitrary spectrum depicted in the top left panel. Theline superimpositions on the histogram in the top right represents aclassical and quantum magnitude superposition. The lower left panel isduplicative of the conventional four photon single evaluation of thearbitrary spectrum (upper left panel) and represents the input signalinto the quantum computer depicted in FIG. 2. The lower right paneldepicts the reconstructed arbitrary spectrum (upper left panel) based onquantum Fourier transform as described herein, followed by an inverseFourier transform. The solid overlapping lines represent reconstructedprobability and classical magnitudes.

Patent documents and publications mentioned in the specification areindicative of the levels of those skilled in the art to which theinvention pertains. These documents and publications are incorporatedherein by reference to the same extent as if each individual document orpublication was specifically and individually incorporated herein byreference.

The terminology “computer” as used herein means processor,microprocessor, CPU, multiprocessor, personal computer or any devicewhich has the capability of performing the functions of a computer.

The foregoing description is illustrative of particular embodiments ofthe invention, but is not meant to be a limitation upon the practicethereof. The following claims, including all equivalents thereof, areintended to define the scope of the invention.

APPENDIX A COMPUTER LISTING

function scqft % Test of Semi-Classical Fourier %%profile onwarning(‘off’, ‘all’) H=hadamard(2)*sqrt(2) /2; %%[ys Fs bits]=wavread(‘hal90005k.wav’); [ys Fs bits]=wavread(‘kennedy_PCMa.wav’);%%[ys Fs bits]=wavread(‘postest2.wav’); %%[ys Fsbits]=wavread(‘chimes.wav’); %[ys Fs bits]=wavread(‘G2.wav’); %%[MMNN]=size(ys) %%%sb=fix(size(ys(512+1:512+2{circumflex over ( )}17)));sb=fix(size(ys)); %%sb=fix(size(ys(1:256))) NBits=fix(log2(sb(1)))+1 %%%TEST %%NBits=10 NBits=19 %%NBits=15 %%ttt=BuildPhase(1,3) pause2{circumflex over ( )}NBits A=zeros(2{circumflex over ( )}NBits,1);AR=A; %%AR(1:2{circumflex over ( )}NBits)=ys(1:2{circumflex over( )}NBits); AR(1:sb(1))=ys(1:sb(1)); %%AR=AR+.1; %%AR=[−sqrt(−.25) .2sqrt(−.6) 1]; %%AR=[1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1]; %%AR=[−sqrt(−1)−.25 .75*sqrt(−1) 1]; %%AR=2*rand(1, 2{circumflex over ( )}NBits−1;%%R=sqrt(AR); AR=AR/sqrt(sum(AR.*conj(AR))); %%AR=transpose(AR);[min(AR) max(AR)] plot(AR) hold on arsize=size(AR) %%pause % OutputSubset wavwrite(AR,Fs,bits, ‘haltest.wav’) AR1=AR-min(AR);AR1=AR1/max(AR1); wavwrite(AR1,Fs,bits,‘haldc.wav’) clear AR1asum=sum(abs(AR)) A=AR; A(1:2{circumflex over ( )}NBits)=0; %%% TEST AR1was AR A(1:1:2{circumflex over ( )}NBits)=AR(1:1:2{circumflex over( )}NBits); size(A) size(AR) clear AR NSamples=5;spectrum=zeros(2{circumflex over ( )}NBits,1); spectrum2=spectrum;posum=spectrum2; A2=A.*conj(A); ‘A2 Sum’ a2sum=sum(A2) sum(A2/a2sum)[min(A2) max(A2)] wavwrite(sqrt(A2),Fs,bits,‘haltest2.wav’)%%plot(sqrt(A2),‘green’) %%hold off %%chunkmx=2{circumflex over ( )}7;%2{circumflex over ( )}4 chunkmx=2{circumflex over ( )}0;%%chunkmx=2{circumflex over ( )}8; %%chunkmx=2{circumflex over ( )}0chunksz=2{circumflex over ( )}NBits/chunkmx ‘Done Readin’ pause %%%forichunk=1:chunkmx %%% [ichunk chunkmx] %%% istart=(ichunk−1)*chunksz+1;%%% istop=istart+chunksz−1; %%% A2T=A(istart:istop);%%% A2Tsum=max(abs(A2T)); %%% spectrum2=fft(A2T);%%% spectrum2=(spectrum2.*conj(spectrum2)); %%% ssum=sum(spectrum2);%%% spectrum2=spectrum2/ssum; %%% spmx=max(spectrum2);%%% A2IF=ifft(sqrt(spectrum2));%%% AO(istart:istop)=real(A2IF)/sum(abs(real(A2IF)));%%% plot(AO(istart:istop),‘red’) %%% hold on%%% plot(A2(istart:istop),‘green’) %%% plot(spectrum2,‘cyan’) %%% holdoff %%% drawnow  %% Normalize%%% AO(istart:istop)=A0(istart:istop)*A2Tsum; %%%end%%%plot(real(AO),‘red’) %%%hold on %%% ‘AO’ %%%[max(real(AO))max(real(A2)*asum)] %%%hold off %%%AO=AO/max(abs(AO+eps));%%%wavwrite(AO,Fs,bits,‘haltest3.wav’) %%pause %%%clear AO %%profile onA2S=A2; A2SSUM=sum(A2S)+eps; A=A/sqrt(A2SSUM); A2S=A.*conj(A); ‘sumtest’ sum(A.*conj(A)) clear A2S CBits=1og2(chunksz) ipend=1; %%% BuildList of U operators for ii=CBits:−1:1   ii   nn=2{circumflex over( )}CBits; mm=nn;   UL(ii).H=BuildU(ii,H); end pause forichunk=1:chunkmx   tic   [ ichunk chunkmx ]  istart=(ichunk−1)*chunksz+1;   istop=istart+chunksz−1;  ipend=ipend+chunksz;   spct1=zeros(2{circumflex over ( )}CBits,1);  posum=spct1;   spctI=spct1;   % Extract Subset of Input Signal andNormalize   A2S=A2(istart:istop);   A2SSUM=sum(A2S) %%% subplot(2,2,3)%%% A2S=A2S/(A2SSUM+eps); %%% bar(A2S/(max(A2S)+eps)) %%% [min(A2S)max(A2S)] %%% a2mx=max(A2S); %%% axis([0 2{circumflex over ( )}CBits+1 01.01])   % Extract Sub-sample for state preparation  A2S=A2(istart:istop);   AIS=A(istart:istop);   % Prepare for QFT  spct1=zeros(2{circumflex over ( )}CBits,1);   posum=spct1;  apsum=posum;   aspct=posum;   A2I=A2S/sum(A2S);   AI=AIS/norm(AIS,2);  AMX=max(abs(A(istart:istop)));   if (sum(AI)~=0)    for IS=1:NSamples    y(1:CBits)=0;     % Start QFT     IB=0;     AN=transpose(AI);    for ii=CBits:−1:1      IB=IB+1;      % Build U for this operation onthe state      %%%U=BuildU(ii,H);      % Multiply U by the current state     %%nn=2{circumflex over ( )}ii; mm=nn;     API=UL(ii).H*transpose(AN);      % Find probabilities     P=API.*conj (API);      % Extract Probabilties of Measuring      %current Qbit in state |1>      isto1=2{circumflex over ( )}ii;     istr1=floor(isto1/2)+1;      P1=sum(P(istr1:isto1));      %Meausure Qubit      y(ii)=MeasureQ(P1);      if(ii ~= 1)       % Extractnew state       if(y(ii)==0)        AN=API(1:istr1−1);       else       AN=API(istr1:isto1);       end       AN=AN/norm(AN,2);       %Build controlled Phase operation       R=BuildPhase(y(ii),CBits−IB);      % Multiply that state by the controlled       % phase      AN=R*AN;       clear R;       AN=transpose(AN);      end     end    str2=num2str(y(CBits:−1:1),‘%ld’);     [str2 ‘ ’ num2str(ichunk) ‘ ’num2str(IS)]     % Store measurements in index basis%%%   subplot(2,2,1);     str=num2str(y(1:CBits),‘%ld’);    indx=fix(bin2dec(str))+1;     spct1(indx)=spct1(indx)+1;    spct1o=(spct1)/IS;     spct1o=spct1/sum(spct1);     %%%bar(spct1o)%%%   hold on %%%   spctmx=max(spct1o);%%%   p2=(abs(fft(A(istart:istop)))); %%%   p2=p2.*conj(p2);%%%   p2=p2/(sum(p2)+eps); %%%   plot(p2,‘green’)%%%   spctmx=max(spctmx,max(p2)); %%%   axis([ 0 2{circumflex over( )}CBits+1 0 spctmx]) %%%   hold off %%%   drawnow     % Fourier Signal%%%    subplot(2,2,4) %%%    piqft=real(ifft(sqrt(spct1))); %%%   piqft=piqft/sum(abs(piqft)); %%%    Piqft=piqft/max(abs(piqft));    %%%bar(piqft) %%%    hold on %%%   ap=AO(istart:istop)/(max(abs(AO(istart:istop)))+eps); %%%    plot(ap,‘green’) %%%    hold off %%%    pmx=max(max(piqft,ap’)); %%%   pmn=min(min(piqft,ap’)); %%%    axis( [0 2{circumflex over( )}CBits+1 pmn−eps pmx+eps]) %%%    drawnow    end   end   ‘AfterSamples’   % Classical IFT   iqft=ifft(sqrt(spct1/NSamples));  signal(istart:istop)=real(iqft)/sum(abs(real(iqft)));  signal(istart:istop)=signal(istart:istop);%*AMX;  a2ssum=sum(A2(istart:istop));   toc end profile off ‘Before FullSignal’ sigmx=max(abs(signal)) signal=signal/sigmx; clfplot(signal,‘red’) drawnow hold on %%plot (real(AO),‘green’)%%plot(A/max(abs(A)),‘cyan’)waywrite(real(signal),Fs,bits,‘qfthalNL.wav’) functionanswer=MeasureQ(prob) s=rand; answer=99; while answer==99   if(s<prob)   answer=1;   else    answer=0;   end end function answer=BuildU(N,H)I=eye(2,2); answer=sparse(H); for i=1:N−1  answer=sparse(kron(answer,I)); end function answer=BuildPhase(y,NQ)isize=2{circumflex over ( )}NQ; %answer=eye(isize,isize);answer=speye(isize); ‘Build Phase’ if (y==1)  for IQ=1:NQ  nchunks=2{circumflex over ( )}(IQ−1);   chunksize=isize/(2*nchunks);  [IQ NQ nchunks chunksize]   afac=exp(i*pi*y/(2{circumflex over( )}IQ));   for ichunk=1:nchunks %%    [ichunk nchunks]   istart=(ichunk*chunksize)+1+(ichunk−1)*chunksize;   istop=istart+chunksize−1;    for IS=istart:istop     c=fix((istop−istart)*.1); %%    if(mod(IS,c)==0) %%     [IS istart istop] %%   end %%    answer(IS,IS)=answer(IS,IS)*exp(i*pi*y/(2{circumflex over( )}IQ));     answer(IS,IS)=answer(IS,IS)*afac;    end   end  end end C

The invention claimed is:
 1. A method of data compression comprising:converting data, with a converter, into n qubits representing 2^((n))bits of data; each qubit having two properties and with each halfweighted for a first and second property respectively; transmitting afirst qubit with a transmitter; measuring the first qubit, with adetector, at a receiver location; determining whether or not to transmitportions of data from a sequential successive qubit based upon the valueof the first qubit measured at the receiver location.
 2. The method ofclaim 1 wherein the data comprises the contents of a message and basedupon the value of the first qubit measured at the receiver location,data compression occurs such that fewer qubits are used to transmit theoriginal contents of a message.
 3. The method of claim 1 wherein thedata comprises information to be transmitted to the receiver and basedupon the value of the first qubit measured at the receiver location,data compression occurs such that fewer qubits are used to represent thedata transmitted without curtailing the information received by thereceiver.
 4. A system for data compression and transmission comprising asender and at least one receiver, the sender comprising: a converter forconverting data into qubits; a modulator for modulating a signal basedupon the values of the qubits; a transmitter for transmitting themodulated signal to at least one receiver; the at least one receivercomprising: a detector for measuring the value of at least one qubit; afeedback circuit for transmitting the measured value of the at least onequbit to the sender; whereby the transmission of data for eachsuccessive qubit is based upon the value measured for the precedingqubit and the sender utilizes only the data for each successive qubitswhich correlates to the measured value of the preceding qubit.
 5. Thesystem of claim 4 wherein for a group of n qubits, the amount of datarepresented by the n^(th) transmitted qubit is ½^((n-1)) the amount ofdata represented by the first transmitted qubit.
 6. The system of claim4 whereby the qubits are interrelated such that the measurement of thepreceding qubit determines what portion of the data is unnecessary datafor the next qubit.
 7. The system of claims 6 wherein the information tobe transmitted is substantially unaffected by the data which is nottransmitted.
 8. The system of claim 7 wherein the data to be transmittedrepresents a sound recording and the transmission of successive qubitswhere the n^(th) transmitted qubit represents only ½^((n-1)) the amountof data represented by the first transmitted qubit does notsignificantly impact the recognizability of the sound recording.
 9. Amethod of transmitting a data signal comprising: (a) dividing a signalinto a series of sections with each section comprising N samples of thesignal; (b) preparing a first qubit from N samples of the signal using aQuantum Fourier transform; (c) passing the qubit though a phase shiftdevice; (d) measuring the qubit and recording the result of themeasurement as a 0 or 1; (e) determining which half of the N samples ofthe current signal section are used as a subsection to prepare the nextqubit, and discarding the remainder; (f) preparing next qubit generatedfrom the original signal section with the next qubit using only half ofthe succeeding signal subsection; (g) passing the succeeding qubitthough a phase shift device; (h) measuring the succeeding qubit andrecording the result of the measurement as a 0 or 1; (i) determiningwhich half of the N samples of the succeeding signal section are used asa subsection to prepare the next qubit, and discarding the remainder;(j) repeating the steps (f) through (i) until the last qubit isprepared.
 10. The process of claim 9 wherein the steps are repeated anumber of times on the same signal section to generate a power spectrumrepresentation of the signal section.
 11. The process of claim 9 whereinthe measurement of all of the qubits for one section produces a binarynumber that indicates the address of the bin addressed by that binarynumber.
 12. A method of data compression comprising: converting data,with a converter, into qubits; transmitting a first qubit with atransmitter; measuring the first qubit, with a detector, at a receiverlocation; determining whether or not to transmit portions of data from asequential successive qubit based upon the value of the first qubitmeasured at the receiver location, wherein based upon the value of tilefirst qubit measured at the receiver location, data compression occurssuch that fewer qubits are used to transmit a message to the receiver.13. The method of claim 12 wherein the data comprises knowledgeinformation in the form of a communication to be sent to the sender andwherein based upon the value of the first qubit measured at the receiverlocation, fewer qubits are used to transmit the information to thereceiver without affecting the content of the knowledge information. 14.The method of claim 12 wherein data is converted into n qubits andwherein for n equal to 3, the first qubit represents a first group offour bins weighted for a first photon characteristic and a second groupof four bins weighted for the conjugate of the first photoncharacteristic; and, depending upon the measured value of the firstqubit, only one half of the data is used to prepare the second qubit,represented by 2^((n-1)) bins for transmission.
 15. The method of claim14 wherein the third qubit may be represented by four groups of twobins, and depending upon the measurement of the second qubit, datarepresented by 2 bins is transmitted and the data represented by theremaining 6 bins is discarded.
 16. The method of claim 12 wherein eachqubit represents 2″ bins of data, and for each successive qubit, datarepresented by the qubit is decreased by a factor of
 2. 17. The methodof claim 12 wherein each qubit is a photon and information istransmitted based upon the polarization of the photon.